Answer:
65 square units
Step-by-step explanation:
Assuming point O refers to the origin, the segment OA has slope ...
m = Δy/Δx = 5/1 = 5
Then the slope of the perpendicular line AP will be the negative reciprocal of this, -1/5.
The x-intercept of the line through (1, 5) with slope -1/5 can be found by setting y=0 in the point-slope equation for that line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
0 -5 = (-1/5)(x -1)
25 = x -1 . . . . . . . multiply by -5
x = 26 . . . . . . . add 1
This means ΔOAP has a base length (OP) of 26 units and an altitude of 5 units. Its area is given by the formula ...
A = 1/2bh
A = 1/2(26)(5) = 65 . . . . square units
Triangle OAP has an area of 65 square units.
B = block p = park
2b + p = 10 min 2 runs around the block takes 10 minutes
2b + 3p = 22 min 2 runs around the block plus 3 runs around the park takes 22 minutes
To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.
2b + p = 10 min ---------→b + 1/2p = 5 ----------→ b = 5 - 1/2p
2(5 - 1/2p) + 3p = 22 ---------→ 10 -p + 3p = 22 --------→ 10 + 2p = 22
10 + 3p = 22 ----------→ 2p = 12
2p = 12 -------------→ p = 6
It takes 6 minutes to jog around the park
Hope this helps!
Answer:
Why is 3 an integer?
They are the numbers you usually count and they will continue on into infinity. Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart e.g. … -4, -3, -2, -1, 0,1, 2, 3, 4
Answer:
3. x=90
6. X= 180-120
X=60
Step-by-step explanation:
hope this helps
